I like your question as it brings back the spirit of "light organs" of the 60's and 70's that inspired so many EE's and music lovers alike.
From your hobby link, I see somewhat bluish high power LEDs ( 1W) which can be chosen for desire in any color but remember the voltage drop changes with color chemistry as it does for battery chemistry. So consult the standard operating tables in specifications for best results, in addition to the maximum values.
I suggest your original p/n the TIP31 is far better than the BC337-40 and here's why.
The LEDs in your link are 1 Watt standard type LEDs that are typically rated in the 350 mA range. The BC337 has a Vce of 0.9V and hFE of 80 @25C @ 350 mA meaning the power rating (250mW) of the part is greatly exceeded and it would burn out with approximately 0.9V*0.35A drop (315 mW). So it fails with too high Vce saturated voltage, too low hFE @ 350mA, even though hFE is high and OK for 20mA LED's it falls from 600 to 80 for these LEDs.
I recommend you put as many LED's as you need in series that will fit with your voltage source by adding up the rated voltages for same current and choosing a power source that is 0.2 to 0.5 or so more than this sum for selecting a current limiting power resistor. Sources of power could be your 12V IDE port or a laptop power source or a wall transformer. If you have more LEDs what would want to add. Put that series string in parallel with the required small ohm current limiting resistor. If you heat sink the TO-220 switch to a large aluminum baseplate with the LEDs and use a tiny fan inside with a vent of 12V.
I can imagine a design that works very well with 12V TIP31 and 3 Blue or White LEDs and using the base resistor and TIP31 gain as the current limiting resistor with a pot.
Many enhancements in the design include using a tuned filter for Bass treble and separate colors of LEDs.
You can use a signal AC bridge diode assembly to rectify the music and I would suggest adding a transistor Common Emitter buffer to drive the TIP31. ( std simple design in web search)
Just find a 3.5mm Jack splitter to connect your speakers and Light Organ. and :) :) have fun... :) :)